A Dynamic Optimal Control Model of Crop Thinning

We develop a general optimal control model of crop thinning applicable to settings in agriculture, horticulture and viticulture. Using a simple optimal control model for the land owner’s profit maximization problem, relevant scenarios are discussed using phase diagram analysis: (1) when the initial crop quantity is sufficiently small, crop thinning is not optimal, (2) when the initial crop quantity is high, it is optimal to thin the crop from the beginning of the relevant planning horizon and to reduce it over time until the stock of the crop has arrived at its optimum. From thereon, crop quantity evolves solely according to natural growth and/or decay. Depending on the model's parameters, this “stopping time” is reached sooner or later.